Find the angle between two lines whose direction ratios are proportional to `1,1,2a n d(sqrt(3)-1),(-sqrt(3)-1),4` .

Explanation

To find the angle between two lines whose direction ratios are proportional to (1, 1, 2) and (√3 - 1, -√3 - 1, 4), we can use the formula for the cosine of the angle θ between two lines given their direction ratios.

### Step-by-Step Solution:

1. **Identify Direction Ratios:**
Let the direction ratios of the first line be \( L_1 = 1, M_1 = 1, N_1 = 2 \).
Let the direction ratios of the second line be \( L_2 = \sqrt{3} - 1, M_2 = -\sqrt{3} - 1, N_2 = 4 \).

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